But you can also go from C down to G. What is that interval called? Hint: it’s not a fifth.

As before, you can count the number of half-steps going down from C to G. Or you can take the elaborate method of counting the number of notes and adjusting for sharps and flats.

But there is another way: you can invert the interval from C-up-to-G to get the interval from C-down-to-G.

Here is the rule: inverted interval = 9 – interval

Fortunately, that is not too heavy on the mathematics. So C-down-to-G is: 9 – 5 = a 4th.

The 5th was perfect. Is our 4th also “perfect”?

A few more rules:

Perfect intervals remain perfect.

Major intervals become minor.

Minor intervals become major.

Augmented becomes diminished.

Diminished becomes augmented.

So inverting a perfect fifth indeed results in a perfect fourth, and vice versa.

Another example: the interval C up to A. This is a major sixth. If we invert this interval, we get 9 – 6 = 3 and major becomes minor. So C-down-to-A is a minor third.

To find an interval in the opposite direction, you can also reverse the notes. Instead of doing C-down-to-G you can consider this G-up-to-C, which is identical. Likewise, C-down-to-A is equivalent to the interval A-to-up-C.